Defeasible Reasoning,
Special Pleading and the Cosmological Argument

Abstract

The rehabilitation of causation and modal realism in recent
analytic philosophy have made possible the revival of the argument
from contingency to the existence of a necessary first cause. Recent
work in defeasible or nonmonotonic logic means that this argument can
be cast in such a way that it does not presuppose that every contingent
situation, without exception, has a cause. Instead, the burden of proof is
shifted to the skeptic, who must produce positive reasons for thinking that
the cosmos is an exception to the defeasible law of causality. The most
promising line of rebuttal open to the skeptic contradicts a
plausible account of the nature of causal priority, namely, that the actuality
of a token
causes is necessitated by the actuality of its token effect. Several independent
lines of argument in support of this account are outlined.

Introduction

The cosmological argument for God's existence has a long history, but perhaps
the most enduring version of it has been the argument
from contingency. This is the version that Frederick Copleston pressed upon
Bertrand Russell in their debate about God's existence in 1948.
In 1997 ("A New Look at the Cosmological Argument, American Philosophical Quarterly34:193-212), I noted that all three of Russell's principal objections to the
argument (viz., the unreality of modality, the unreality of causation, and
the unreality of the world as a totality) have fared poorly in recent analytic
philosophy.
This is especially clear in the case of causation.
Far from withering away (as Russell anticipated), the notions of cause and
effect have never held a
more central position.
Causality is absolutely central to recent philosophical work in
semantics, the philosophy of mind and intentionality, epistemology, and
philosophy of science.

The Cosmological Argument

The formal framework I employed in "A New Look at the
Cosmological Argument" was a modal logic
supplemented by the Lesniewski-Goodman-Leonard
calculus of individuals ("mereology") .
By way of modal logic, I needed only the axioms and rules of T.
I used the two usual predicate symbols of mereology, P and
O, representing part-of and overlap,
respectively. I needed three mereological axioms :

Axiom 1 x P y (z )(z O x ->
z O y)

Axiom 2E x C(x) -> E y (z) ( z O y
E u ( C(u) & u O z)).

Axiom 3 x = y (x P y & y P x)

Axiom 1 defines the part-of relation in terms of overlap, and Axiom 2 is an
aggregation or fusion principle: if there are any situations of type C,
then there is
an aggregate or sum of all the C situations. Axiom 3 guarantees that the
part-of relation is reflexive and anti-symmetric.
There were two principles linking the modal and mereological languages. Here
I needed to introduce a new predicate, A. Where b is a possible situation,
Ab can be
used to state that b actually obtains.

Axiom 4 x P y -> Nec ( Ay -> Ax).

Axiom 5 Nec( (y)( Fy -> Ay) -> ASum(x):Fx)

Axiom 4 ensures that aggregation of situations is a form of conjunction:
a whole
necessitates all of its parts. Conversely, 5 implies that the existence
of all the members of a sum necessitates the existence of the sum itself.
There is one special notion that had to be defined: that of being "wholly
contingent," represented by W.

DefinitionW x (Ax & (y)(y P x ->
-NecAy))

A wholly contingent situation is an actual situation none of whose parts
are necessary.
Finally, I needed only three facts about causation:

Axiom 6 (Veridicality)
(x => y ) -> (Ax & Ay)

Axiom 7 (Separate Existence) (x => y) -> -(x O y)

Axiom 8 (Universality) (x)( Wx -> E y (y => x))

Axiom 6 stipulates that only actual situations can serve as causes or effects.
Axiom 7 is intended to capture Hume's insight that a cause and its effect
must be "separate existences." The language of mereology, when applied
to situations, enables us to state Hume's principle precisely: a cause must not
overlap its effect. It is very important to bear in mind that Axiom 6 does
not require that a cause must not overlap its effect in space or time: it is only
mereological overlap (the having of a common part) that is ruled out.
Axiom 8 expresses the universality of the causal relation:
every wholly contingent situation has a cause. Axiom 8 does not entail determinism,
in any of its usual senses, since I have not stated that causes are sufficient
conditions for their effects. I do not assume that every event is
necessitated by its causes; in fact, I believe that this is not typically
the case. For this reason, this account of causation
is compatible with indeterministic theories of human freedom and
indeterministic interpretations of quantum mechanics.

In "A New Look at the Cosmological Argument" , I used these
axioms to prove the following theorem:

Theorem. If there are any contingent situations, then the cosmos (the
sum of all wholly contingent situations) has a cause that is a necessary
situation.

Since we know that there is at least one contingent situation, we can
use Theorem 1 to conclude that the cosmos has a cause
that is a necessary situation, a First Cause. It is legitimate to call this
cause a "first cause" if we assume (as seems plausible) that all effects are
contingent.

The Role of Defeasible Reasoning

Even though we
have excellent empirical evidence for the generalization that wholly
contingent situations have causes, it is hard to see how any amount of
data could settle conclusively the question of whether or not this
generalization (Axiom 8) admits of exceptions. The skeptic can always
find a logically consistent position by simply restricting the scope of
axiom 8 in such a way as to exclude its application to the cosmos as a whole.

The most effective response, dialectically speaking, is
to insist that, at the very least, our
experience warrants adopting the causal principle as a default or
defeasible rule. This means that, in the absence of evidence to the
contrary, we may infer, about any particular wholly contingent situation, that it
has a cause.

This is, however, all that is needed for the cosmological argument to be
rationally compelling. In place of a deductively valid, apodeictic proof
of the existence of a first cause, the defender of the cosmological
argument can offer instead a defeasible argument (an argument correct
by the standards of nonmonotonic reasoning).
The burden is then shifted to the agnostic, who must
garner evidence of a positive sort for the proposition that the cosmos really
is an exception to the rule. Merely pointing out the defeasible nature of the
inference (i.e., the bare possibility of the cosmos's being an
exception) does not constitute a cogent rebuttal.

Considerable progress has been made in recent year in developing formal
systems of defeasible or nonmonotonic reasoning that satisfy certain
plausible meta-logical constraints. For example, in the Commonsense Entailment
system of Asher and Morreau, a defeasible version of Axiom 8 could be
expressed by using a default conditional connective, >:

Axiom 8* (x)( Wx > E y (y => x))

This version of Axiom 8 can be read as: normally, a wholly contingent
situation has a cause.
This defeasible Axiom 8* will allow us
to infer that any given wholly contingent situation has a
cause unless some positive reason can be given for thinking that the situation
in question is an exception to the rule, for example, by showing that the
situation belongs to a category of things that typically does not
have a cause.

The skeptic could refuse to accept even the defeasible generalization
8*. Like Kant or Russell, he might insist that the universality of
causation be seen as a canon or
prescriptive rule for reason, and not as a descriptive
generalization (even a defeasible one) of mind-independent
reality.

However, to give up even the defeasible version of Axiom 8 as a
descriptive generalization about reality is to embrace a radical
form of skepticism. All of our
knowledge about the past, in history, law and natural science, depends on
our inferring causes of present situations (traces, memories, records). Without the
conviction that all (or nearly all) of these have causes, all of our
reconstructions of the past (and therefore, nearly all of our knowledge of
the present) would be groundless. Moreover, our knowledge of the future and
of the probably consequences of our actions depends on the assumption that the
relevant future states will not occur uncaused. The price of denying this
axiom is very steep: embracing a comprehensive Pyrrhonian skepticism.

The Best Rebuttal to the Argument

In my 1997 article, I dealt with twelve objections to the cosmological
argument, including the classic Humean and Kantian objections. Here I would
like to focus on what I take to be
the most promising rebuttal to the defeasible
version of the cosmological
argument. This rebuttal is based on making the simple
observation, Don't contingent situations
typically have contingent
causes? This is an instance of a wider strategy: focus on some unique
feature of the First Cause and point out the cause of the world's having
that feature is an exception to some well-established generalization. Indeed,
for the most part, contingent situations do have contingent causes. They also
have causes with finite attributes and causes that can be located in space
and time, features which, in each case, the hypothesized First Cause would
lack.

Once we have established that
the the cause of the cosmos would be relevantly unusual, we seem to be faced with two equally
unattractive options: supposing that the cosmos has only a very unusual kind of
cause, or supposing that it has no cause at all. Thus, we seem to
end in a stalemate.

This is essentially
the line taken by Graham Oppy in his recent response to my original
paper. Oppy defines a first event as
a situation to which nothing is temporally prior. Oppy argues that we could replace Axiom 8*
with the principle that every non-first event has a cause (call this Axiom
8NF). Oppy contends that all the evidence that can be adduced in support
of Axiom 8* can also be adduced in support of 8NF, so there is
no ground for preferring one to the other (Oppy, p. 381).

Oppy admits that his principle is "slightly less natural" than Axiom 8*
(p. 388 n. 5). I would argue that Oppy's principle is
"slightly less natural" than Axiom 8* in exactly the same way that
all emeralds are grue is "slightly less natural" than
all emeralds are green. When drawing inductive generalizations,
any loss of naturalness, no matter how "slight," can be
critical. In fact, Oppy's restriction of the universality
of causation to non-first events is a classic case of special pleading, until
and unless he can provide some principled ground for thinking that the
absence of temporally prior situations is relevant to the presence or
absence of a cause.

Oppy seems confused here about the nature of
defeasible or nonmonotonic reasoning. It is certainly logically
consistent to maintain the universality of causation with the exception of
first events, but Oppy has not shown that it is reasonable to
maintain such an exception. If Oppy's only reason for excepting first events
from the scope of Axiom 8 is his distaste of the conclusion which would
otherwise be drawn (viz., the existence of a necessary first cause), then
his position is consistent but unreasonable, just as it would be unreasonable
for me to except the events that occur after January 1, 2001. It would be
consistent for me to maintain that all events except those occurring
after January 1, 2001 have causes, and my version of Axiom 8, which we
might call Axiom 8Y2K is supported by exactly the same body of evidence
supporting Axiom 8*, but clearly it would be unreasonable to except
those events without providing some positive reason to think that
the temporal location of an event relative to the turn of the millennium is
relevant to its being caused or uncaused.

Although Oppy offers no defense for his restriction of the scope of
Axiom 8*, there are several defenses that could be mounted.
A defender of Oppy's principle could perhaps appeal to Hume's account of
the nature of causal priority. If the causal priority of an event to one
of its effects simply consists in its temporal priority to that effect,
then we would have very good reason for supposing that first events have
no causes, since nothing could be causally prior to them. However, there
are good reasons to resist Hume's account of the nature of
causal priority. First, it excludes the possibility of temporally backwards
causation, which seems to be metaphysically possible and has actually
figured in scientific explanations and interpretations of quantum mechanics.
Second, the nature of temporal priority is even more obscure than that of
causal priority, and the best accounts of temporal priority seem to be
those that presuppose the ontologically prior existence of causal priority.

A second line of defense of Oppy's principle would be to point out that
all of the causes with which we are familiar are temporally prior to their
effects. In Realism Regained, I provide a number
of arguments for thinking that this is mistaken: that we do, in fact,
have experience of the causal efficacy of atemporal situations (such as
the situations that support the holding of certain natural laws).
Moreover, even if this claim were correct about our experience,
it would fail to support Oppy's principle, since what we
need is a positive reason for thinking that situations that are not
temporally related to an event cannot cause it. Merely observing
that all of the causes we are familiar with in experience are temporally
prior to their effects does not support Oppy's principle if our experience is
in fact limited to temporally located
situations. We can only observe that situations do have
temporal causes; we cannot observe that they do not have
atemporal causes, but it is the latter observation that would be needed
to justify Oppy's restriction of Axiom 8*. Consider the following
analogy:
all the causes we have so far observed occurred before January 1,
2001, but this gives us no reason to think that all causes without
exception will occur before this date.

However, there is a third, more successful line of defense for Oppy's
principle. All of the situations we have observed have had causes
which were at least in part located in time at a moment earlier than
the effect. Oppy's first events are clearly unusual in this respect: if
they have any causes, these causes cannot be located even in part at a
time prior to the first event.

This third version of a defense of Oppy's principle can be subsumed under
the original objection I mentioned: namely, that all observed cases of
causation are cases in which the cause was contingent. In
my 1997 paper, I argued that necessary (non-contingent) situations cannot
be located in space or time (pp. 199-200). If I can explain
why we must conclude, this fact notwithstanding, that the cosmos has a necessary
cause, then I will have also explained why we must conclude that first
events have non-temporal causes, since necessary causes are ipso facto
atemporal ones.

In other words, the defender of the cosmological argument must respond
to this sort of rebuttal with substantial reasons
for thinking that, although the First Cause is unique in a number of
respects, each of these unique features can be adequately explained by
extrapolating from tendencies already observable in ordinary cases of causation.
My own defense of the argument is based on the following
thesis: that, in some precise sense, a cause is always
more necessary (or, equivalently, less contingent) than its effect.

In other words, a situation a is more necessary than situation b just
in case a
is actual in every world in which any part of b is actual, but a could
be actual in the absence of the actuality of any part of b. This follows from
the identity
conditions of situations. The causes of a situation are essential to its identity:
had the very same truth been verified by a situation caused in a different way, we
would not have had the same situation as verifier.
The corresponding thesis involving effects is not plausible: a situation's
identity does not include the eventuality of all its effects.

This assumption is a generalization of the Kripkean intuition that the
origin of a thing is always essential to it.
It is true that in
natural language we sometimes treat event-tokens with slightly different
parts and antecedents as identical. For example, we might say that
the death of Caesar would have been less painful had Brutus not participated.
However, such looseness in natural language should not be taken as
settling the metaphysical issue.

This principle (an effect necessitates the existence of its causes) does not
imply that the content or intrinsic type
of an effect necessitates the content or type of its
causes. For example, the token situation
of Caesar's death could not have existed had not
all of its causes, including Brutus' knife-thrust, existed. This of course does
not mean that Caesar wouldn't have died unless Brutus and the other senators
had killed him. The truth `Caesar died' would have been verified by a different
situation in all of those worlds in which Brutus does not help in inflicting the
fatal set of wounds. The situation that actually verifies the truth `Caesar died'
would not have existed had any of its causes failed to exist.

There are several additional reasons for thinking that causes are more necessary than
their effects. First, it is clear that we need some account of causal
priority that explains the transitivity and asymmetry of this relation.
An account of causal priority in terms of relative contingency nicely
satisfies this desideratum.

Second, this account enables us to specify
exhaustively the potential causes of a given situation: a is a potential
cause of b if and only if a is more necessary (less contingent) than b. Such a specification is necessary if we are to
account for the statistical properties of causal connections, the
so-called "Markovian principles"
developed by Salmon
and Suppes,
and studied recently by Pearl and Verma
and Spirtes, Glymour and Scheines.
I use these
Markovian principles in developing a causal calculus in Appendix B of
my forthcoming book.
Markov locality entails that the causal antecedents of an event "screen off"
the probability of that event from the probability of any non-consequent
event-token. If we assume that the probability of every actual event-token
is screened off in this way
by its actual causes, then we are implicitly assuming that the
causal antecedents of any actual token are necessary to its identity, that
there are no non-actual or counterfactual causes of actual tokens.

Finally, this principle seems to be implicit in our conviction that the
past is fixed
and the future is open.
The relative necessity of causally antecedent tokens gives us an
explanation of the asymmetry of past and future. The fixity
of the past can best be understood as the relative necessity of past event-tokens,
given the token event corresponding to the present.
This thesis is
implicit in all "branching-future" models of temporal logic.

The cosmos (as I have defined it) is a situation
of absolutely minimal contingency. If situation a contains situation b
as a part, then b
is no less contingent (no more necessary) than a, since (by Axiom 4)
a could not be actual
if b were not actual. Since the cosmos contains every wholly contingent
situation
as a part, no wholly contingent situation can be less contingent than the
cosmos.

Since the cosmos
is a situation of minimal contingency, it is not surprising that it should
have no contingent cause, but it would still be very surprising if it had
no cause at all. By extrapolating from our common experience with causation,
we conclude that a situation of minimal contingency (such as the cosmos) has
a non-contingent (necessary) cause. At the same time, the principle of causal
priority as asymmetric necessitation gives us good reason for concluding that
the necessary cause of the cosmos is itself uncaused, since nothing can
be strictly more necessary than an absolutely necessary situation.

These considerations lead to a new version of the critical Axiom 8:

Axiom 8**
(x)(Wx >
Ey (y is more necessary than x & y => x))

On the basis of induction, we can confirm that, at every degree of
necessity (short of absolute necessity), every token is caused by some
token more necessary than it. As we successfully build scientific models that stretch
across astronomical and geological time, we confirm that
situation-tokens across a wide swath of degrees of necessity
have causes that are strictly more necessary than themselves.
Axiom 8** is the generalization
of this pattern (in the form of a defeasible rule).
Axiom 8** states that we
may reasonably infer, about any token at any degree of contingency, that it
has a causal antecedent which is more necessary than it.

We can now give an adequate justification for the restriction of causality to wholly contingent situations. If we substitute any situation that is not wholly contingent (that contains at least one necessary part) for x in the consequent of Axiom 8**, the result is necessarily false, since there is no situation more necessary than an absolutely necessary
situation. Consequently, the generalized defeasible axiom couldn't be true without the restriction in the antecedent to wholly contingent situations. Any further restriction, along the lines advocated by Oppy, would have to be justified on other grounds.

When we apply Axiom 8** to the Cosmos, or to any other
minimally contingent situation, we succeed in drawing the defeasible
conclusion that it has a cause, and
in addition, we have an explanation as to why the cause of the
Cosmos is necessary.